The Growth Rate Along the Balanced-Growth Path
Economies that have not yet accumulated enough capital to be on their balanced-growth paths will have a growth rate that equals the balanced-growth rate plus an additional factor due to the growth rate of capital relative to GDP. [3]
output per worker growth rate
= balanced-growth output-per-worker growth rate + a
1−a × (capital growth rate−output growth rate) .
The first term is the growth rate along the balanced-growth path. The second term is the additional component to growth that comes about whenever the capital stock is growing faster than output. Table 6.6 “Approaching the Balanced-Growth Path” gives an example of an economy that is approaching a balanced-growth path. Like the economy. “Output and Capital Stock in a Balanced-Growth Economy”, the balanced-growth output growth rate is 3 percent. The workforce grows at 1 percent, so output per worker grows at 2 percent along the balanced- growth path. However, this economy starts off (in the year 2000) with a smaller capital stock than is needed for balanced growth. Looking at the first row of the table, you can see that the capital stock grows at 14.4 percent, while output grows at 6.8 percent. Because capital grows faster than output, there is an additional component to growth, as we have just explained. This contributes an extra 3.8 percentage points to the growth rate, so output per worker grows at 5.8 percent. As time goes on, the capital stock grows relative to output, and the economy gets closer to the balanced-growth path. As this happens, the additional component of growth becomes smaller. For example, in 2010, the capital stock grows at 6.8 percent, and output grows at 4.3 percent. The growth rate of output per worker is 3.3 percent—2 percentage points being the balanced- growth contribution and 1.3 percent due to the faster growth rate of capital stock compared to output. By 2050, the economy is close to balanced growth: output per worker grows at 2.3 percent, with capital stock growing only a little bit faster than output.
